A tank is 7 metre long and 4 meter wide wide. At what speed should water run through a pipe 5 cm broad and 4 cm deep so that in 6 hours and 18 minutes water level in the tank rises by 4.5 meter?

Explanation:-

$$\eqalign{ & {\text{Rate of flow of water}} \cr & {\text{ = }}x{\text{ cm/minutes}} \cr & \therefore {\text{Valume of water that flowed in the in1 minutes}} \cr & {\text{ = 5}} \times {\text{4 }} \times x{\text{ = 20}}x\,\,{\text{cu}}{\text{.cm}} \cr & \therefore {\text{Valume of water that flowed in the in}} \cr & {\text{6 hours 18 minutes }} \cr & {\text{i}}{\text{.e}}{\text{. }}\left( {6 \times 60 + 18} \right) = 378\,\min \cr & = \,{\text{ 2}}x \times 378{\text{ cu}}{\text{.cm}} \cr & {\text{According to question, }} \cr & {\text{20}}x \times 378 = 700 \times 400 \times 450 \cr & \Rightarrow x = \left( {\frac{{700 \times 400 \times 450}}{{20 \times 378}}} \right){\text{cm /minutes}} \cr & \Rightarrow x = \left( {\frac{{700 \times 400 \times 450 \times 60}}{{100000 \times 20 \times 378}}} \right){\text{km/hours}} \cr & \Rightarrow x{\text{ = 10 km/hours}} \cr}$$